Domain controlled piezoelectric single crystal and fabrication method therefor

ABSTRACT

A domain controlled piezoelectric single crystal is disclosed which uses a lateral vibration mode for an electromechanical coupling factor k 31  not less than 70% and a piezoelectric constant −d 31  not less than 1200 pC/N, with an electromechanical coupling factor k 33  in the longitudinal vibration mode not less than 80% and a piezoelectric constant d 33  not less than 800 pC/N. Also, a piezoelectric single crystal is disclosed which uses a high-performance longitudinal vibration mode with k 31  not more than 30%. A fabrication method applies a DC electric field of 400 V/mm to 1500 V/mm for a maximum of two hours in a temperature range of 20° C. to 200° C. as polarization conditions in the thickness direction of the piezoelectric single crystal. The method can include cooling, or heating and cooling between temperature boundaries of rhombohedral and tetragonal crystals or between tetragonal and cubic crystals or within a cubic crystal temperature range.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a piezoelectric single crystaland a fabrication method therefor. More particularly, the inventionrelates to a piezoelectric single crystal which is developed payingattention to an electromechanical coupling factor in a directionperpendicular to the polarization direction, i.e., a lateral vibrationmode, and domain control in that direction, and a fabrication methodtherefor.

[0003] 2. Description of the Related Art

[0004] With regard to a piezoelectric single crystal, for example,Japanese Patent Laid-Open No. 38963/1994 discloses an ultrasonic probeusing a piezoelectric material comprised of a solid solution singlecrystal of lead zinc niobate-lead titanate. This technique provides aprobe with a high sensitivity by using that single crystal of such apiezoelectric material which has an electromechanical coupling factor(k₃₃) of 80 to 85% in a direction parallel to the polarizationdirection. While the electromechanical coupling factors in the directionparallel to the polarization direction of piezoelectric single crystalshave been studied and various usages have been developed conventionally,the characteristics in a direction perpendicular to the polarizationdirection have not been studied yet.

[0005] The present inventors paid attention to the facts that apiezoelectric single crystal is adapted to multifarious usages for theelectromechanical coupling factor (k₃₃) in a direction parallel to thepolarization direction (longitudinal vibration mode) of thepiezoelectric single crystal has a value equal to or greater than 80%,the electromechanical coupling factor (k₃₁) in a direction perpendicularto the polarization direction (lateral (=length extensional) vibrationmode) is, for example, 49% to 62%, lower than the electromechanicalcoupling factor k₃₃ in the direction parallel to the polarizationdirection (longitudinal vibration mode), as described in pp. 239 in IEEEProc. MEDICAL IMAGING 3664 (1999) and other documents, and that theelectromechanical coupling factor k₃₁ takes a value that varies from onedocument to another. Through intensive studies on the phenomenon, theinventors discovered that it would be possible to fabricate apiezoelectric single crystal and their devices which would effectivelyuse the electromechanical coupling factor k₃₁ in case where theelectromechanical coupling factor k₃₃ in the direction parallel to thepolarization direction (longitudinal vibration mode) was equal to orgreater than 80%, a piezoelectric constant d₃₃ was equal to or greaterthan 800 pC/N, the electromechanical coupling factor k₃₁ was equal to orgreater than 70% and a piezoelectric constant −d₃₁ was equal to orgreater than 1200 pC/N (d₃₁ having a negative value by definition), andwould be possible to fabricate a piezoelectric single crystal and theirdevices which would use the value of k₃₃ more efficiently due togeneration of no spurious (undesired vibration) or the like in the bandof usage of that value in case where k₃₃ was equal to or greater than80%, d₃₃ was equal to or greater than 800 pC/N, k₃₁ was equal to orsmaller than 30% and −d₃₁ was equal to or smaller than 300 pC/N (d₃₁having a negative value by definition).

[0006] Further, the inventors discovered that the cause for thepiezoelectric single crystal to have an intermediate electromechanicalcoupling factor k₃₁ in the direction perpendicular to the polarizationdirection (lateral vibration mode) and to have a variation in the factorwhile having a large electromechanical coupling factor k₃₃ in thedirection parallel to the polarization direction (longitudinal vibrationmode) was that the domain structure formed by an electric dipoleassociated with the direction perpendicular to the polarizationdirection of a polarized piezoelectric single crystal was formed byplural domains (multiple domains), not a single domain, and that thefollowing piezoelectric single crystals (A) and (B) were obtained bycontrolling the domain structure.

[0007] (A) A domain controlled piezoelectric single crystal having anelectromechanical coupling factor k₃₃≧80% in the longitudinal vibrationmode and a piezoelectric constant d₃₃≧800 pC/N, comprising anelectromechanical coupling factor k₃₁≧70% in a lateral vibration mode, apiezoelectric constant −d₃₁≧1200 pC/N and a frequency constant fc₃₁(=fr·L)≦650 Hz·m which is a product of a resonance frequency fr in thelateral vibration mode relating to k₃₁ and a length L of thepiezoelectric single crystal in a vibration direction.

[0008] (B) A domain controlled piezoelectric single crystal having anelectromechanical coupling factor k₃₃24 80% in a longitudinal vibrationmode and a piezoelectric constant d₃₃≧800 pC/N, comprising anelectromechanical coupling factor k₃₁≦30% in a lateral vibration mode ina direction perpendicular to the polarization direction, a piezoelectricconstant −d₃₁≦300 pC/N and a frequency constant fc₃₁ (=fr·L)≧800 Hz·mwhich is a product of a resonance frequency fr in the lateral vibrationmode relating to k₃₁ and a length L of the piezoelectric single crystalin a vibration direction.

[0009] The inventors also found that the conditions for controlling thedomain structure were rearranged based on the value of a frequencyconstant fc₃₁ (=fr·L), which is a product of the resonance frequency frin the lateral vibration mode relating to k₃₁ and the length L of thepiezoelectric single crystal in the vibration direction.

[0010] The invention aims at providing such a piezoelectric singlecrystal and a fabrication method therefor.

SUMMARY OF THE INVENTION

[0011] According to the first aspect of the invention, there is provideda domain controlled piezoelectric, single crystal having anelectromechanical coupling factor k₃₃≧80% in a longitudinal vibrationmode and a piezoelectric constant d₃₃≧800 pC/N, comprising anelectromechanical coupling factor k₃₁≧70% in a lateral vibration mode, apiezoelectric constant −d₃₁≧1200 pC/N (d₃₁ has a negative value bydefinition) and a frequency constant fc₃₁ (=fr·L)≦650 Hz·m which is aproduct of a resonance frequency fr in the lateral vibration moderelating to k₃₁ and a length L of the piezoelectric single crystal in avibration direction.

[0012] According to the second aspect of the invention, there isprovided a domain controlled piezoelectric single crystal having anelectromechanical coupling factor k₃₃≧80% in a longitudinal vibrationmode and a piezoelectric constant d₃₃≧800 pC/N, comprising anelectromechanical coupling factor k₃₁≦30% in a lateral vibration mode, apiezoelectric constant −d₃≦300 pC/N (d₃₁ has a negative value bydefinition) and a frequency constant fc₃₁ (=fr·L) ≧800 Hz·m which is aproduct of a resonance frequency fr in the lateral vibration moderelating to k₃₁ and a length L of the piezoelectric single crystal in avibration direction.

[0013] The lengthwise direction of, for example, a rod-likepiezoelectric single crystal with an aspect ratio of 3 or greater is thepolarization direction and the vibration in the direction parallel tothe polarization direction (longitudinal vibration) when a voltage isapplied in the polarization direction and the efficiency of conversionbetween electrical and mechanical energy are respectively expressed bythe electromechanical coupling factor k₃₃ in longitudinal vibration modeand the piezoelectric constant d₃₃. The greater those values are, thehigher the efficiency is. Those values are also defined forpiezoelectric single crystals with other shapes, such as a plate and adisc shape, besides the rod-like one. The invention pertains to a domaincontrolled piezoelectric single crystal developed paying attention tothe electromechanical coupling factor k₃₁ in the direction perpendicularto the polarization direction (lateral vibration mode).

[0014] It is possible to use the following materials as thepiezoelectric single crystal material according to the first aspect ofthe invention or the second aspect of the invention.

[0015] (a) A solid solution which is comprised of X·Pb (A₁, A₂ , . . . ,B₁, B₂ , . . . )O₃+(1−X)PbTiO₃(0<X<1) where A₁, A₂ , . . . are one orplural elements selected from a group of Zn, Mg, Ni, Lu, In and Sc andB₁, B₂ , . . . are one or plural elements selected from a group of Nb,Ta, Mo and W, and in which a sum ω of valencies of elements inparentheses in a chemical formula Pb(A_(1Y1) ^(a1), A_(2Y2) ^(a2) , . .. , B_(1Z1) ^(b1), B_(1Z2) ^(b2) , . . . )O₃ satisfies charges ofω=a₁·Y₁+a₂·Y₂+ . . . b₁·Z₁+b₂·Z₂+ . . . =4+ where a₁, a₂ , . . . arevalencies of A₁, A₂ , . . . , b₁, b₂ , . . . are valencies of B₁, B₂ , .. . and Z₁, Z₂ , . . . are composition ratios in the chemical formula.

[0016] (b) The material (a) added with 0.5 ppm to 1% by mass of one ortwo of Mn and Cr.

[0017] The best known materials are piezoelectric single crystalmaterials comprised of solid solutions of lead zinc niobatePb(Zn_(1/3)Nb_(2/3))O₃ or lead magnesium niobate Pb(Mg_(1/3)Nb_(2/3))O₃and lead titanate PbTiO₃ (the former combination is called “PZN-PT” or“PZNT” and the latter one “PMN-PT” or “PMNT”).

[0018] The following are methods of fabricating the above-describeddomain controlled piezoelectric single crystals.

[0019] The first one is a piezoelectric single crystal fabricatingmethod of fabricating a domain controlled piezoelectric single crystal,comprising a step of applying a DC electric field of 400 V/mm to 1500V/mm for a maximum of two hours in a temperature range of 20° C. to 200°C. as polarization conditions in a thickness direction of thepiezoelectric single crystal or a step of cooling while applying anelectric field (field applied cooling).

[0020] While this method performs final polarization of a domaincontrolled piezoelectric single crystal device such as actuators,sensors and transducers, it is effective to employ a piezoelectricsingle crystal device such as actuators, sensors and transducersfabricating method which, prior to the final polarization step,additionally comprises a step of applying an electric field in adirection perpendicular to the polarization direction of a piezoelectricsingle crystal and a step of controlling a direction of a ferroelectricdomain perpendicular to the polarization direction. The types ofelectric fields to be applied in the direction perpendicular to thepolarization direction include steady electric fields, such as a DCelectric field, a pulse electric field and an AC electric field, and anattenuating electric field. There are different proper conditions forthe intensities of the electric fields, the application times,temperatures and so forth depending on the characteristics of eachpiezoelectric single crystal and the desired value of theelectromechanical coupling factor k₃₁ in the direction perpendicular tothe polarization direction. Those conditions can be determined byexperiments, etc. As the pulse electric field, a unipolar pulse, such asa rectangular wave, and a bipolar pulse, such as an (AC) triangular wavecan be used.

[0021] Another method of the invention is characterized by heating andcooling a piezoelectric single crystal before a step of finalpolarization of a domain controlled piezoelectric single crystal, whichapplies a DC electric field of 400 V/mm to 1500 V/mm for a maximum oftwo hours in a temperature range of 20° C. to 200° C. or performscooling while applying an electric field (field applied cooling). Forexample, the temperature ranges for a piezoelectric single crystal tobecome rhombohedral, tetragonal and cubic are determined in accordancewith the composition. Therefore, as a step (1) of heating and cooling apiezoelectric single crystal material with a temperature of transitionbetween a rhombohedral crystal which is in a low temperature phase ofthe piezoelectric single crystal and a tetragonal crystal which is in anintermediate temperature phase of the piezoelectric single crystalmaterial in between, or a step (2) of heating and cooling thepiezoelectric single crystal material between a Curie temperature T_(c)(the piezoelectric single crystal material becomes cubic over the T_(c)with the disappearance of the ferroelectricity) and a rhombohedralcrystal in the low temperature phase or a tetragonal crystal in theintermediate temperature phase, or a step (3) of heating and cooling thepiezoelectric single crystal material in a temperature range of a cubiccrystal which is in a high temperature phase equal to or higher than theT_(c), or a step (4) of adequately combining the steps (1),(2) and (3)is executed followed by a step of applying a DC electric field of 400V/mm to 1500 V/mm for a maximum of two hours in a temperature range of20° C. to 200° C. or performing cooling while applying an electricfield, it is possible to control the aligned state of ferroelectricdomains perpendicular to the polarization direction.

[0022] Further, before a step of applying a DC electric field of 400V/mm to 1500 V/mm for a maximum of two hours in a temperature range of20° C. to 200° C. or performing cooling while applying an electricfield, a step of applying an electric field in a direction perpendicularto the polarization direction of a piezoelectric single crystal and astep of heating and cooling the piezoelectric single crystal are usedtogether, followed by a step of applying a DC electric field of 400 V/mmto 1500 V/mm for a maximum of two hours in a temperature range of 20° C.to 200° C. or performing cooling while applying an electric field, it ispossible to control the aligned state of ferroelectric domainsperpendicular to the polarization direction.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023]FIG. 1 is an exemplary perspective view of a crystal structure;

[0024]FIG. 2 is a phase diagram of PZN-PT (PZNT);

[0025]FIG. 3 is an explanatory diagram of application of an electricfield;

[0026]FIG. 4 is a diagram of an impedance curve and phase in k₃₁vibration mode;

[0027]FIG. 5 is a diagram of an impedance curve and phase in k₃₁vibration mode;

[0028]FIG. 6 is a diagram of an impedance curve and phase in k₃₁vibration mode;

[0029]FIG. 7 is a diagram of an impedance curve and phase in k₃₁vibration mode;

[0030]FIG. 8 is a diagram of an impedance curve and phase in k₃₁vibration mode;

[0031]FIG. 9 is a diagram showing the state of a domain structure in aplane in the polarization direction (thickness direction) afterapplication of an electric field;

[0032]FIG. 10 is a graph of the values of an electromechanical couplingfactor k₃₁ and a frequency constant (fc₃₁=fr·L) which is the product ofa resonance frequency fr in k₃₁ vibration mode and the length (L) of thepiezoelectric single crystal in a vibration direction;

[0033]FIG. 11 is an explanatory diagram of application of an electricfield;

[0034]FIG. 12 is a k₃₃ vs. d₃₃ graph; and

[0035]FIG. 13 is a waveform diagram of a bipolar triangular pulse.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0036] For example, the unit lattice of the solid solution singlecrystal of lead zinc niobate-lead titanate (PZN-PT or PZNT) has aperovskite structure (ABO₃) as exemplarily shown in FIG. 1. FIG. 2presents a phase diagram of PZN and PT. This diagram is picked up fromNomura et al., J. Phys. (1969), or J. Kuwata et al., Ferroelectrics(1981). As seen from FIG. 2, rhombohedral PZNT has a spontaneouspolarization equivalent to an electric bipolar in eight directions ofthe orientation <111> of a crystal when it is seen as a pseudo cubic.When an electric field is applied in the direction <100> (crystalcutting direction) in such a spontaneous polarization state, theelectric bipolar rotates in the direction of applying a polarizationelectric field so that the spontaneous polarization directions arealigned.

[0037] However, it was found that the alignment took various statesdepending on the mode of applying the electric field, resulting in thatalthough the electromechanical coupling factor k₃₃ in the directionparallel to the polarization direction had a value equal to or greaterthan 80%, the electromechanical coupling factor k₃₁ in the directionperpendicular to the polarization direction was distributed with avariation of 49 to 62% as described in the documents or the like, i.e.,that with respect to the direction perpendicular to the polarizationdirection (lateral vibration mode), the electromechanical couplingfactor k₃₁ was not controlled. With such a value of k₃₁, it wasdifficult to prepare a device positively using k₃₁. Also with such avalue of k₃₁, a piezoelectric single crystal positively using k₃₃ hadmany responses called spurious generated in the longitudinal vibration(k₃₃) mode in the direction of parallel to the polarization direction,so that sufficient characteristics could not obtained. The factors thatwould give such results are explained as follows. In the material of thepiezoelectric single crystal cut out of the piezoelectric single crystalafter its as grown state, the domains comprised of a set of electricbipolars of the same direction face various directions in the directionparallel to the polarization direction and the direction perpendicularto the polarization direction, and do not show a piezoelectricity andare in an unpolarized state.

[0038] Multi domains cannot be aligned in the direction parallel to thepolarization direction unless an ordinary polarization temperature andapplied voltage are selected and an electric field is applied in thedirection parallel to the polarization direction. Accordingly, theelectromechanical coupling factor k₃₃ in the polarization directionshows a large value equal to or greater than 80%. However, the states ofthe domains in the direction perpendicular to the polarization directioncan be controlled only under the polarization conditions in thedirection parallel to the polarization direction, i.e., only within theadequate ranges of the polarization temperature and the applied voltage.

[0039] A method of controlling the mode of polarization direction willnow be discussed referring to some examples. Table 1 shows thedielectric/piezoelectric characteristics of the single crystals in casewhere the polarization conditions or the like for prior arts (sampleNos. 1, 2 and 3), document values (document values 1 and 2) and thepiezoelectric single crystal material according to the invention arevaried. The values of d₃₃ in Table 1 were measured by a d₃₃ meter (ZJ-3Dtype produced by Chugoku Kagakuin Seigaku Kenkyujyo). The k₃₃ valueswere computed from the d₃₃ vs k₃₃ curve shown in FIG. 12 based on themeasurements made by the present inventors. k₃₁, d₃₁, and fc₃₁ werecomputed from the frequency response of the impedance measured. FIGS. 4through 8 illustrate impedance curves in k₃₁ mode after individualelectric fields of 250 V/mm (sample No. 4), 500 V/mm (sample No. 5), 700V/mm (sample No. 6), 1000 V/mm (sample No. 7) and 1600 V/mm (sample No.8) were applied, for ten minutes between electrodes of a piezoelectricsingle crystal plate in use (device dimensions:13 mm long×4 mm wide×0.36 mm thick) with 0.91PZN+0.09PT (X=0.91 expressed by a molarfraction) prepared by forming gold electrodes on two opposing (001)faces 11 of a crystal 10 by sputtering as shown in FIG. 3 and dippingthe resultant structure in a silicon oil of 40° C. The polarization isinsufficient in case of 250 V/mm (FIG. 4), and three responses regardingk₃₁ vibration modes are seen for 500 V/mm (FIG. 5) and 700 V/mm (FIG.6), because there are multi domains in the direction perpendicular tothe polarization direction.

[0040] (Table 1)

[0041] For 1000 V/mm (FIG. 7), as apparent from the impedance curve,there is a single response, i.e., single domain in the directionperpendicular to the polarization direction and the k₃₁ value satisfiesto be greater than 80% and k₃₃ in the direction parallel to thepolarization direction shows a value over 95%. For 1600 V/mm (FIG. 8),dividing the single response into two or three responses, the domain isseparated again into two or more domains and k₃₃ in the directionparallel to the polarization direction shows a value over 95% while thek₃₁ value is 61%. The value of the frequency constant fc₃₁ (=fr·L) whichis a product of the resonance frequency fr in the lateral vibration moderelating to k₃₁ of each sample and the length L (13 mm long) of thepiezoelectric single crystal in the vibration direction was 741 Hz·m forthe sample No. 4, 601 Hz·m for the sample No. 5, 603 Hz·m for the sampleNo. 6, 522 Hz·m for the sample No. 7 and 700 Hz·m for the sample No. 8.FIG. 9 shows the state of the domain structure in a plane perpendicularto the polarization direction after application of electric fields of250 V/mm, 500 V/mm, 1000 V/mm and 1600 V/mm.

[0042] In FIG. 9, while polarization is insufficient for 250 V/mm andthere are multi domains for 500 V/mm, k₃₁ becomes larger due to thesynergism of the polarization components relating to k₃₁. There is asingle domain for 1000 V/mm and k₃₁ become maximum, and there are multidomains for 1600 V/mm, and k₃₁ becomes smaller due to the counteractionof the polarization components relating to k₃₁. In the invention, thedomain layouts that would provide high k₃₃ (d₃₃) and high k₃₁ (d₃₁) werethose for 500 V/mm and 1000 V/mm. When the temperature of the siliconoil was dropped to room temperature while applying a DC electric fieldof 400 V/mm to a piezoelectric single crystal with the same setting andthe sample No. 9 in the silicon oil temperature of 200° C., theelectromechanical coupling factor k₃₃ in the direction parallel to thepolarization direction (longitudinal vibration mode) was equal to orgreater than 80% and the electromechanical coupling factor k₃₁ in thedirection perpendicular to the polarization direction (lateral vibrationmode) was greater than 70%. The fc₃₁ at this time was 609 Hz·m. For thesample No. 10, a piezoelectric single crystal with the same setting wasdipped into the silicon oil of 60° C., and a DC electric field of 400V/mm was applied to the piezoelectric single crystal for 120 minutes. Asa result, while the electromechanical coupling factor k₃₃ in thedirection parallel to the polarization direction (longitudinal vibrationmode) was greater than 95%, the electromechanical coupling factor k₃₁ inthe direction perpendicular to the polarization direction (lateralvibration mode) was less than 30%.

[0043] For the sample No. 11, when a DC electric field of 1500 V/mm wasapplied to a piezoelectric single crystal with the same setting for 10minutes, the electromechanical coupling factor k₃₃ in the directionparallel to the polarization direction (longitudinal vibration mode) wasgreater than 90% by contrast with the electromechanical coupling factork₃₁ in the direction perpendicular to the polarization direction(lateral vibration mode) being less than 30%. fc₃₁ for the sample No. 10and the sample No. 11 were respectively 981 Hz·m and 1004 Hz·m. It seemsthat the results have originated from the domain layout that suppressthe lateral vibration.

[0044] By adequately setting the polarization conditions (appliedvoltage, temperature, etc.) this way, it is possible to control thedomain state and the values of k₃₃ and k₃₁ that depend on the domainstate. The invention is not limited to this embodiment, but it wasconfirmed that dielectric/piezoelectric characteristics similar to thoseof the embodiment described above could be acquired by using thetemperature range, the polarization direction electric field range, theapplication time range and the application method for the step ofapplying a DC electric field of 400 V/mm to 1500 V/mm for a maximum oftwo hours in a temperature range of 20° C. to 200° C. or performingcooling while applying an electric field.

[0045] Further, with regard to the step of applying a DC electric fieldof 400 V/mm to 1500 V/mm for a maximum of two hours in a temperaturerange of 20° C. to 200° C. or performing cooling while applying anelectric field, it was confirmed that the characteristics of the firstaspect and second aspect of the invention were improved also byrepeating the step of applying a DC electric field of 400 V/mm to 1500V/mm for a maximum of two hours in a temperature range of 20° C. to 200°C. or performing cooling while applying an electric field with adepolarization step of holding at 200° C. higher than the Curietemperature for one hour in between. It was found that by arrangingthose results based on the frequency constant fc₃₁ (=fr·L), the productof electromechanical coupling factor k₃₁ in the direction perpendicularto the polarization direction (lateral vibration mode), the resonancefrequency fr in k₃₁ mode and the length L of the piezoelectric singlecrystal in the vibration direction, a domain with high k₃₃ and high k₃₁and a domain with high k₃₃ and low k₃₁ shown in FIG. 10 were obtainedwith the range of the value of the frequency constant fc₃₁ (=fr·L) onthe horizontal axis in FIG. 10.

[0046] The prior arts and the document values are also given in FIG. 10.According to the prior arts and the document values, the frequencyconstant fc₃₁ (=fr·L) which is the product of the resonance frequency frin k₃₁ mode and the length L of the piezoelectric single crystal in thevibration direction lies between the values given in appended claims 1and 2. It seems that, as clarified in the foregoing description of theinvention, the k₃₁ value varies because the domain control in thedirection perpendicular to the polarization direction is insufficient.

[0047] Referring now to Table 2, a description will be given of anembodiment in which a step of applying an electric field in thedirection perpendicular to the polarization direction of a piezoelectricsingle crystal and controlling the direction of the ferroelectric domainstructure in the direction perpendicular to the polarization direction,a step (1) of heating and cooling a piezoelectric single crystalmaterial with a temperature of transition between a rhombohedral crystalwhich is in a low temperature phase of the piezoelectric single crystaland a tetragonal crystal which is in an intermediate temperature phaseof the piezoelectric single crystal material in between, or a step (2)of heating and cooling the piezoelectric single crystal material betweena Curie temperature T_(c) and a rhombohedral crystal in the lowtemperature phase or a tetragonal crystal in intermediate temperaturephase, or a step (3) of heating and cooling the piezoelectric singlecrystal material in a high temperature phase equal to or higher than theT_(c), or a step (4) of adequately combining the steps (1), (2) and (3)was carried out, followed by a step of applying a DC electric field of400 V/mm to 1500 V/mm for a maximum of two hours in a temperature rangeof 20° C. to 200° C. or performing cooling while applying an electricfield. The measurement of d₃₃, the computation of the k₃₃ value, and themeasurement and computation of k₃₁, d₃₁ and fc₃₁ in Table 2 are similarto those in Table 1.

[0048] For the sample No. 12, before the step of applying a DC electricfield of 400 V/mm to 1500 V/mm for a maximum of two hours in atemperature range of 20° C. to 200° C. or performing cooling whileapplying an electric field, gold electrodes were formed on two (010)faces 13 of a piezoelectric single crystal of the same shape with thatof the aforementioned single crystal, which were opposite to each otherand were perpendicular to the (001) faces 11 in FIG. 3 by sputtering asshown in FIG. 11, a DC electric field of 1000 V/mm was applied to theresultant structure in the silicon oil of 40° C. for ten minutes forpolarization. After the piezoelectric single crystal was removed fromthe silicon oil bath, the gold electrodes were removed by an etchingsolution and gold electrodes are further formed on the two opposing(001) faces 11 shown in FIG. 3 by sputtering, the step of applying a DCelectric field of 400 V/mm to 1500 V/mm for a maximum of two hours in atemperature range of 20° C. to 200° C. indicated in the above-describedembodiment or performing cooling while applying an electric field wascarried out, and then the dielectric/piezoelectric characteristics weremeasured.

[0049] As a result, the electromechanical coupling factor k₃₃ of 97.3%in the direction parallel to the polarization direction (longitudinalvibration mode) and the piezoelectric constant d₃₃ of 2810 pC/N wereobtained as shown in the sample No. 12 in Table 2. Further, theelectromechanical coupling factor k₃₁ of 85.5% in the directionperpendicular to the polarization direction (lateral vibration mode) andthe piezoelectric constant d₃₁ of −2380 pC/N were obtained. The value ofthe frequency constant fc₃₁ (=fr·L) which is a product of the resonancefrequency fr in the lateral vibration mode in the directionperpendicular to the polarization direction relating to k₃₁ and thelength L of the device in the vibration direction was 483 Hz·m.

[0050] For the sample Nos. 13, 14 and 15, before the step of applying aDC electric field of 400 V/mm to 1500 V/mm for a maximum of two hours ina temperature range of 20° C. to 200° C. or performing cooling whileapplying an electric field, piezoelectric single crystals of the sameshapes with that of the aforementioned single crystal were dipped in thesilicon oil, and temperature increasing and decreasing were repeatedthree times in a cycle of 30 minutes in the temperature ranges of 50 to90° C. and 150 to 200° C. in the silicon oil and further in thetemperature range of 200 to 400° C. in an electric oven. Thereafter,gold electrodes were formed on two opposing (001) faces 11 shown in FIG.3 by sputtering, a step of applying a DC electric field of 400 V/mm to1500 V/mm to the resultant structure in the temperature range of 20° C.to 200° C. indicated in the above-described embodiment for a maximum oftwo hours or performing cooling while applying an electric field wascarried out, and then the dielectric/piezoelectric characteristics weremeasured. As a result, the electromechanical coupling factor k₃₃ of97.5% in the direction parallel to the polarization direction(longitudinal vibration mode) and the piezoelectric constant d₃₃ of 2840pC/N were obtained for the sample No. 13.

[0051] The electromechanical coupling factor k₃₁, of 85.3% in thedirection perpendicular to the polarization direction (lateral vibrationmode) and the piezoelectric constant d₃₁ of −2360 pC/N were obtained.For the sample No. 14, the electromechanical coupling factor k₃₃ of97.8% in the direction parallel to the polarization direction(longitudinal vibration mode) and the piezoelectric constant d₃₃ of 2880pC/N were obtained.

[0052] The electromechanical coupling factor k₃₁ of 85.3% in thedirection perpendicular to the polarization direction (lateral vibrationmode) and the piezoelectric constant d₃₁ of −2350 pC/N were obtained.For the sample No. 15, the electromechanical coupling factor k₃₃ of97.4% in the direction parallel to the polarization direction(longitudinal vibration mode) and the piezoelectric constant d₃₃ of 2820pC/N were obtained. The electromechanical coupling factor k₃₁ of 85.6%in the direction perpendicular to the polarization direction (lateralvibration mode) and the piezoelectric constant d₃₁ of −2380 pC/N wereobtained. The frequency constant fc₃₁ (=fr·L) was 503 Hz·m for thesample No. 13, was 506 Hz·m for the sample No. 14 and was 437 Hz·m forthe sample No. 15, respectively.

[0053] For the sample No. 16, gold electrodes were formed on twoopposing (010) faces 13 perpendicular to the (001) faces 11 in FIG. 3were formed by sputtering as shown in FIG. 11, the piezoelectric singlecrystal was dipped in the silicon oil, and a DC electric field of 400V/mm was applied while repeating temperature increasing and decreasingwere repeated three times in a cycle of 30 minutes in the temperaturerange of 150 to 200° C. After the piezoelectric single crystal wasremoved from the silicon oil bath, the gold electrodes were removed byan etching solution and gold electrodes are further formed on the twoopposing (001) faces 11 shown in FIG. 3 by sputtering, the step ofapplying a DC electric field of 400 V/mm to 1500 V/mm for a maximum oftwo hours in a temperature range of 20° C. to 200° C. or performingcooling while applying an electric field was carried out, and then thedielectric/piezoelectric characteristics were measured. As a result, theelectromechanical coupling factor k₃₃ of 97.8% in the direction parallelto the polarization direction (longitudinal vibration mode) and thepiezoelectric constant d₃₃ of 2870 pC/N were obtained. Further, theelectromechanical coupling factor k₃₁ of 86.0% in the directionperpendicular to the polarization direction (lateral vibration mode) andthe piezoelectric constant d₃₁ of −2450 pC/N were obtained. The value ofthe frequency constant fc₃₁ (=fr·L) was 415 Hz·m.

[0054] It was confirmed that the same advantages were obtained even ifthe step of applying a DC electric field of 400 V/mm to 1500 V/mm for amaximum of two hours in a temperature range of 20° C. to 200° C. orperforming cooling while applying an electric field after a DC electricfield was applied between the (100) faces in FIG. 11 as another opposingfaces perpendicular to the (001) faces in FIG. 3.

[0055] For the sample No. 17, before the step of applying a DC electricfield of 400 V/mm to 1500 V/mm for a maximum of two hours in atemperature range of 20° C. to 200° C. or performing cooling whileapplying an electric field, gold electrodes were formed on two (010)faces 13 of a piezoelectric single crystal of the same shape with thatof the aforementioned single crystal, which were opposite to each otherand were perpendicular to the (001) faces 11 in FIG. 3 by sputtering asshown in FIG. 11, a bipolar triangular electric field with a peak valueof 500 V/mm and a period of 800 msec was applied to the resultantstructure in the silicon oil of 60° C. for ten minutes. FIG. 13 showsthe bipolar triangular waveform. After the piezoelectric single crystalwas removed from the silicon oil bath, the gold electrodes were removedby an etching solution and gold electrodes are further formed on the twoopposing (001) faces 11 shown in FIG. 3 by sputtering, the step ofapplying a DC electric field of 400 V/mm to 1500 V/mm for a maximum oftwo hours in a temperature range of 20° C. to 200° C. or performingcooling while applying an electric field was carried out, and then thedielectric/piezoelectric characteristics were measured. As a result, theelectromechanical coupling factor k₃₃ of 97.1% in the direction parallelto the polarization direction (longitudinal vibration mode) and thepiezoelectric constant d₃₃ of 2780 pC/N were obtained. Further, theelectromechanical coupling factor k₃₁ of 18.3% in the directionperpendicular to the polarization direction (lateral vibration mode) andthe piezoelectric constant d₃₁ of −230 pC/N were obtained. The value ofthe frequency constant fc₃₁ (=fr·L) was 863 Hz·m.

[0056] For the sample Nos. 18, 19 and 20, before the step of applying aDC electric field of 400 V/mm to 1500 V/mm for a maximum of two hours ina temperature range of 20° C. to 200° C. or performing cooling whileapplying an electric field, piezoelectric single crystals of the sameshapes with that of the aforementioned single crystal were dipped in thesilicon oil, and temperature increasing and decreasing were repeatedthree times in a cycle of 5 minutes in the temperature ranges of 50 to90° C., 150 to 200° C. in the silicon oil bath and 200 to 400° C. in theelectric oven. Thereafter, gold electrodes were formed on two opposing(001) faces 11 shown in FIG. 3 by sputtering, a step of applying a DCelectric field of 400 V/mm to 1500 V/mm to the resultant structure inthe temperature range of 20° C. to 200° C. indicated in theabove-described embodiment for a maximum of two hours or performingcooling while applying an electric field was carried out, and then thedielectric/piezoelectric characteristics were measured.

[0057] As a result, for the sample No. 18, the electromechanicalcoupling factor k₃₃ of 97.0% in the direction parallel to thepolarization direction (longitudinal vibration mode) and thepiezoelectric constant d₃₃ of 2760 pC/N were obtained. Further, theelectromechanical coupling factor k₃₁ of 18.6% in the directionperpendicular to the polarization direction (lateral vibration mode) andthe piezoelectric constant d₃₁ of −260 pC/N were obtained. For thesample No. 19, the electromechanical coupling factor k₃₃ of 97.3% in thedirection parallel to the polarization direction (longitudinal vibrationmode) and the piezoelectric constant d₃₃ of 2810 pC/N were obtained.Further, the electromechanical coupling factor k₃₁ of 17.8% in thedirection perpendicular to the polarization direction (lateral vibrationmode) and the piezoelectric constant d₃₁ of −190 pC/N were obtained.

[0058] For the sample No. 20, the electromechanical coupling factor k₃₃of 97.2% in the direction parallel to the polarization direction(longitudinal vibration mode) and the piezoelectric constant d₃₃ of 2790pC/N were obtained. Further, the electromechanical coupling factor k₃₁of 18.2% in the direction perpendicular to the polarization direction(lateral vibration mode) and the piezoelectric constant d₃₁ of −220 pC/Nwere obtained respectively. The frequency constant fc₃₁ (=fr·L) was 836Hz·m for the sample No. 18, was 892 Hz·m for the sample No. 19 and was847 Hz·m for the sample No. 20, respectively.

[0059] For the sample No. 21, gold electrodes were formed on twoopposing (010) faces 13 perpendicular to the (001) faces 11 in FIG. 3 bysputtering as shown in FIG. 11, the piezoelectric single crystal wasdipped in the silicon oil, and a DC electric field of 400 V/mm wasapplied while repeating temperature increasing and decreasing wererepeated three times in a cycle of 5 minutes in the temperature range of150 to 200° C. After the piezoelectric single crystal was removed, thegold electrodes were removed by an etching solution and gold electrodesare further formed on the two opposing (001) faces 11 shown in FIG. 3 bysputtering, the step of applying a DC electric field of 400 V/mm to 1500V/mm for a maximum of two hours in a temperature range of 20° C. to 200°C. or performing cooling while applying an electric field was carriedout, and then the dielectric/piezoelectric characteristics weremeasured. As a result, the electromechanical coupling factor k₃₃ of97.7% in the direction parallel to the polarization direction(longitudinal vibration mode) and the piezoelectric constant d₃₃ of 2850pC/N were obtained. Further, the electromechanical coupling factor k₃lof 17.6% in the direction perpendicular to the polarization direction(lateral vibration mode) and the piezoelectric constant d₃₁ of −150 pC/Nwere obtained. The value of the frequency constant fc₃₁ (=fr·L) was 924Hz·m.

[0060] As the method of controlling the aligned state of ferroelectricdomains perpendicular to the polarization direction by applying anelectric field in the direction perpendicular to the polarizationdirection before the step of final polarization of the domain controlledpiezoelectric single crystal, i.e., the step of applying a DC electricfield of 400 V/mm to 1500 V/mm for a maximum of two hours in atemperature range of 20° C. to 200° C. or performing cooling whileapplying an electric field, the method of controlling the aligned stateof ferroelectric domains perpendicular to the polarization direction bycarrying out the step (1) of heating and cooling a piezoelectric singlecrystal material with a temperature of transition between a rhombohedralcrystal which is in a low temperature phase of the piezoelectric singlecrystal and a tetragonal crystal which is in an intermediate temperaturephase of the piezoelectric single crystal material in between, or thestep (2) of heating and cooling the piezoelectric single crystalmaterial between a Curie temperature T_(c) (the piezoelectric singlecrystal material becomes cubic over the T_(c) with the disappearance ofthe ferroelectricity) and a rhombohedral crystal in the low temperaturephase or a tetragonal crystal in the intermediate temperature phase, orthe step (3) of heating and cooling the piezoelectric single crystalmaterial in high temperature phase equal to or higher than the T_(c), orthe step (4) of adequately combining the steps (1), (2) and (3), and themethod of controlling the aligned state of ferroelectric domainsperpendicular to the polarization direction by carrying out both thestep of applying an electric field in the direction perpendicular to thepolarization direction of the piezoelectric single crystal and the stepof heating and cooling the single crystal piezoelectric device areexecuted, multi domains in the crystal to be produced in the gradualcooling process at the time of growing the crystal are controlled morebased on human efforts. As confirmed, those methods were effective tomore easily control the domain structure in the direction perpendicularto the polarization direction in the step of final polarization of adomain controlled piezoelectric single crystal for fabricating thedomain controlled piezoelectric single crystal and to improve thedielectric/piezoelectric characteristics as mentioned in the foregoingdescription of the first and second aspects of the invention.

[0061] As the domain controlled piezoelectric single crystal accordingto the invention has the above-described structure and the method offabricating the same comprises the above-described steps, it is possibleto fabricate a piezoelectric single crystal which effectively uses theelectromechanical coupling factor k₃₁ in case where theelectromechanical coupling factor k₃₃ in the direction parallel to thepolarization direction (longitudinal vibration mode) is equal to orgreater than 80%, a piezoelectric constant d₃₃ is equal to or greaterthan 800 pC/N, the electromechanical coupling factor k₃₁ is equal to orgreater than 70% and a piezoelectric constant −d₃₁ is equal to orgreater than 1200 pC/N (d₃₁ having a negative value by definition), andit is possible to use the value of k₃₃ more efficiently due togeneration of no spurious (undesired vibration) or the like in the bandof usage of that value in case where k₃₃ is equal to or greater than80%, d₃₃ is equal to or greater than 800 pC/N, k₃₁ is equal to orsmaller than 30% and −d₃₁ is equal to or smaller than 300 pC/N (d₃₁having a negative value by definition). TABLE 1 Polarization conditionsDielectric/piezoelectric characteristics Adapted Temperature Electricfield Time k₃₃ d₃₃ k₃₁ d₃₁ fc₃₁ claims or Sample No. ° C. E V/mm min %10⁻¹² C/N % 10⁻¹² C/N Hz · m the like 1 20 1800 10 95.6 2550 61.5 −970701 Prior art 2 60 400 150 95.3 2500 48.7 −694 773 Prior art 3 100 300120 94.0 2360 35.0 −520 755 Prior art 4 40 250 10 56.0 165 18.9 −224 741insufficient polarization 5 40 500 10 84.0 1190 76.0 −1310 601 Claim 1 640 700 10 87.0 1420 77.1 −1324 603 Claim 1 7 40 1000 10 95.3 2500 80.8−1701 522 Claim 1 8 40 1600 10 95.3 2500 60.9 −939 700 Claim 1 9 200 400Field 80.2 960 74.7 −1263 609 Claim 1 cooling 10 60 400 120 96.9 274026.3 −288 981 Claim 2 11 20 1500 10 94.6 2300 27.1 −291 1004 Claim 2Document 94 2300 53 −1100 — value 1 Document 90 1734 49 −962 680-733value 2 (average value: 707)

[0062] TABLE 2 Dielectric/piezoelectric characteristics Adapted SampleProcess k₃₃ d₃₃ k₃₁ d₃₁ fc₃₁ claims or No. contents Conditions % 10⁻¹²C/N % 10⁻¹² C/N Hz · m the like 12 Claim 5 DC electric field 1000 V/mm,40° C., 10 min 97.3 2810 85.5 −2380 483 Claim 1 13 Claim 6 50-90° C.,cycle of 30 mm, repeated 3 times 97.5 2840 85.3 −2360 503 Claim 1 14Claim 6 150-200° C., cycle of 30 mm, repeated 3 times 97.8 2880 85.3−2350 506 Claim 1 15 Claim 6 200-400° C., cycle of 30 mm, repeated 3times 97.4 2820 85.6 −2380 437 Claim 1 16 Claim 7 DC electric field 400V/mm, 150-200° C., cycle of 97.8 2870 86.0 −2450 415 Claim 1 30 min,repeated 3 times 17 Claim 5 bipolar triangular wave 500 V/mm, cycle 800ms, 97.1 2780 18.3 −230 863 Claim 2 10 min 18 Claim 6 50-90° C., cycleof 5 min, repeated 3 times 97.0 2760 18.6 −260 836 Claim 2 19 Claim 6150-200° C., cycle of 5 min, repeated 3 times 97.3 2810 17.8 −190 892Claim 2 20 Claim 6 200-400° C., cycle of 5 min, repeated 3 times 97.22790 18.2 −220 847 Claim 2 21 Claim 7 DC electric field 400 V/mm,150-200° C., cycle of 97.7 2850 17.6 −150 924 Claim 2 5 min, repeated 3times

What is claimed is:
 1. A domain controlled piezoelectric single crystalhaving an electromechanical coupling factor k₃₃≧80% in a longitudinalvibration mode in the direction parallel to a polarization direction anda piezoelectric constant d₃₃24 800 pC/N, comprising, anelectromechanical coupling factor k₃₁≧70% in a lateral vibration mode ina direction perpendicular to said polarization direction, apiezoelectric constant −d₃₁1200 pC/N and a frequency constant fc₃₁(=fr·L)≦650 Hz·m which is a product of a resonance frequency fr in saidlateral vibration mode in said direction perpendicular to saidpolarization direction relating to k₃₁ and a length L of said device ina vibration direction.
 2. A domain controlled piezoelectric singlecrystal having an electromechanical coupling factor k_(33≧80)% in alongitudinal vibration mode in the direction parallel to a polarizationdirection and a piezoelectric constant d₃₃≧800 pC/N, comprising, anelectromechanical coupling factor k₃₃≦30% in a lateral vibration mode ina direction perpendicular to said polarization direction, apiezoelectric constant −d₃₁≦300 pC/N and a frequency constant fc₃₁(=fr·L) ≧800 Hz·m which is a product of a resonance frequency fr in saidlateral vibration mode in said direction perpendicular to saidpolarization direction relating to k₃₁ and a length L of said device ina vibration direction.
 3. The domain controlled piezoelectric singlecrystal according to claim 1 or 2, wherein said piezoelectric singlecrystal material is either one of following materials (a) and (b): (a) asolid solution which is comprised of X-Pb (A₁, A₂, . . . , B₁, B₂, . . .) O₃+(1−X)PbTiO₃(0<X<1) where A₁, A₂, . . . are one or plural elementsselected from a group of Zn, Mg, Ni, Lu, In and Sc and B₁, B₂ , . . .are one or plural elements selected from a group of Nb, Ta, Mo and W,and in which a sum ω of valencies of elements in parentheses in achemical formula Pb(A_(1Y1) ^(a1), A_(2Y2) ^(a2) , . . . , B_(1Z1)^(b1), B_(1Z2) ^(b2) , . . . )O₃ satisfies charges of ω=a₁·Y₁+a₂·Y₂ +. .. b₁·Z₁+b₂·Z₂+ . . . =4+ where a₁, a₂ , . . . are valencies of A₁, A₂, .. . , b₁, b₂, . . . are valencies of B₁, B₂ , . . . and Z₁, Z₂ , . . .are composition ratios in said chemical formula, and (b) said material(a) added with 0.5 ppm to 1% by mass of one or two of Mn and Cr.
 4. Apiezoelectric single crystal fabricating method of fabricating a domaincontrolled piezoelectric single crystal, comprising, a step of applyinga DC electric field of 400 V/mm to 1500 V/mm for a maximum of two hoursin a temperature range of 20° C. to 200° C. as polarization conditionsin a thickness direction of said piezoelectric single crystal or a stepof cooling while applying an electric field.
 5. The piezoelectric singlecrystal fabricating method according to claim 4, wherein said domaincontrolled piezoelectric single crystal is fabricated by performing astep of applying an electric field in a direction perpendicular to apolarization direction of a piezoelectric single crystal, a step ofcontrolling a direction of a ferroelectric domain perpendicular to saidpolarization direction, and said step recited in claim
 4. 6. Apiezoelectric single crystal fabricating method according to claim 4,wherein domain controlled piezoelectric single crystal is fabricated bycontrolling a direction of a ferroelectric domain perpendicular to apolarization direction of a piezoelectric single crystal by performing astep (1) of heating and cooling a piezoelectric single crystal materialwith a temperature of transition between a rhombohedral crystal which isin a low temperature phase of said piezoelectric single crystal deviceand a tetragonal crystal which is in an intermediate temperature phaseof said piezoelectric single crystal material in between, or a step (2)of heating and cooling said piezoelectric single crystal materialbetween a Curie temperature and a rhombohedral crystal or a tetragonalcrystal, or a step (3) of heating and cooling said piezoelectric singlecrystal material in a temperature range of a cubic crystal which is in ahigh temperature phase equal to or higher than said Curie temperature,or a step (4) of adequately combining said steps (1), (2) and (3),andsaid step recited in claim
 4. 7. A piezoelectric single crystalfabricating method of fabricating a domain controlled piezoelectricsingle crystal comprising the steps of: a step of applying an electricfield in a direction perpendicular to said polarization direction of apiezoelectric single crystal , a step (1) of heating and cooling apiezoelectric single crystal material with a temperature of transitionbetween a rhombohedral crystal which is in a low temperature phase ofsaid piezoelectric single crystal and a tetragonal crystal which is inan intermediate temperature phase of said piezoelectric single crystalmaterial in between, or a step (2) of heating and cooling saidpiezoelectric single crystal material between a Curie temperature and arhombohedral crystal or a tetragonal crystal, or a step (3) of heatingand cooling said piezoelectric single crystal material in a temperaturerange of a cubic crystal which is in a high temperature phase equal toor higher than said Curie temperature, or a step (4) of adequatelycombining said steps (1), (2) and (3), then a step of applying a DCelectric field of 400 V/mm to 1500 V/mm for a maximum of two hours in atemperature range of 20° C. to 200° C. or performing cooling whileapplying an electric field, whereby controlling a direction of aferroelectric domain perpendicular to a polarization direction of apiezoelectric single crystal.